Abstract We analyze an extension for the Fourier law to describe the heat propagation in non-homogeneous solids by taking into accounts simultaneously different diffusion regimes such as the subdiffusion and superdiffusion. It considers differential operators of non-integer order, i.e., fractional differential operators, which are a simple way, from the formal point of view, of understanding the photothermal phenomena, especially the ones obtained with photoacoustic techniques, for a media with these characteristics. Our analysis considers the heat transfer in solid materials by a pulsed light source by considering superdiffusive elements in a subdiffusive matrix. The photoacoustic signal generated by the rear incidence of light (OPC technique) was determined and the influence of superdiffusive and subdiffusive effects was analyzed.

中文翻译：

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光热现象中超和亚扩散行为之间的相互作用

摘要 我们分析了傅立叶定律的扩展，以通过同时考虑不同的扩散方式（例如亚扩散和超扩散）来描述非均质固体中的热传播。它考虑了非整数阶微分算子，即分数微分算子，从形式的角度来看，这是一种简单的方式来理解具有这些特性的介质的光热现象，尤其是通过光声技术获得的光热现象。我们的分析通过考虑亚扩散矩阵中的超扩散元素来考虑脉冲光源在固体材料中的传热。确定了由后入射光（OPC技术）产生的光声信号，并分析了超扩散和亚扩散效应的影响。